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On o-minimal homotopy groups

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Baro González, Elías and Otero, Margarita (2010) On o-minimal homotopy groups. Quarterly Journal of Mathematics , 61 (3). pp. 275-289. ISSN 0033-5606

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Abstract

We work over an o-minimal expansion of a real closed field. The o-minimal homotopy groups of a definable set are defined naturally using definable continuous maps. We prove that any two semialgebraic maps which are definably homotopic are also semialgebraically homotopic. This result together with known results on semialgebraic homotopy allows us to develop an o-minimal homotopy theory. In particular, we obtain o-minimal versions of the Hurewicz theorems and the Whitehead theorem.


Item Type:Article
Uncontrolled Keywords:O-minimal homotopy groups
Subjects:Sciences > Mathematics > Algebra
ID Code:14480
Deposited On:30 Jan 2012 08:21
Last Modified:06 Feb 2014 10:02

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